1)
Z = R + 1/(jwC) = R - j/(wC)
|Z| = RCarrée(R² + 1/(w²C²)) = (1/(wC)) * Rcarrée(1 + w²R²C²)
arg(Z) = arctg(-1/(wRC)) = - arctg(wRC)
u =
Z.
i|u| = |Z|*|i|
arg(
u) = arg(
Z) + arg(
i)
Um = Im * (1/(wC)) * Rcarrée(1 + w²R²C²)
0 = - arctg(wRC) + arg(i)
Phi = arg(i) = arctg(wRC)
***********
2)
Méthode analogue au 1
1/
Z = 1/R + 1/(jwL)
Z = jwLR/(R+jwL)
|Z| = ...
arg(Z) = ...
u =
Z.
i...
*************
3)
1/
Zth = 1/(jwL) + jwC
Zth = jwL/(1-w²L²C²)
Donc Zth est équivalente à l'impédance d'une inductance L' = L/(1-w²L²C²)
Uth/(1/jwC)) = e/(jwL + (1/(jwC))
Uth = e/(1-w²LC)
Et on a aussi ZNorton = Zth
et iNorton = U(th)/Z(th) = e/(jwL)
Si e = Em.sin(wt) --> L.diNorton/dt = Em.sin(wt)
iNorton = Em/(wL) . cos(wt)
***********
4)
R + jwL = 1/((1/R' + 1/(jwL'))
R + jwL = jwL'R'/(R'+jwL')
(R + jwL) * (R'+jwL') = jwL'R'
RR' - w²LL' + j(wLR' + wL'R) = jwL'R'
RR' - w²LL'=0
wLR' + wL'R = wL'R'
...
L' = (R²+w²L²)/(w²L)
R' = (R²+w²L²)/R
****************
Toutes erreurs incluses, rien vérifié.